Aircraft: LARGE TRANSPORT; LOW WING; 2 TURBOJET ENG
Phase of flight: Final Approach
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance

We were cleared to land. There was parallel traffic that was cleared to land on the right parallel runway. Prior to our clearance we called the field and not the traffic in sight for the visual approach. At approximately 2;000 feet; as we were getting established on glide slope; the First Officer who was the Pilot Monitoring noticed Aircraft Y flying very close to us and queried ATC to verify he was cleared to land on the right runway and not the left runway as it looked like he was lining up with our runway. As he queried; we got a TCAS RA. The autopilot was on and I called TCAS blue as the plane reacted to the RA and descended at a rate of about 1;800 FPM. Aircraft Y was now descending on our path above us; so close that we knew he was not lined up with the right runway and was lining up with the left runway. The First Officer told ATC we were responding to an RA and the Tower just replied 'Roger' and did not instruct Aircraft Y to go-around. The First Officer again queried ATC and said are you sure Aircraft Y is lined up with the right runway; which Tower replied; 'Yes Aircraft Y is lined up…oh; it looks like Aircraft X is getting a little nervous.'The plane leveled at 1;200 feet and was almost about to do another descend RA when I clicked off the autopilot because we were so close to the ground and I lined the plane up to the left of the runway to get away from Aircraft Y. The First Officer saw Aircraft Y bank away when he had queried the second time about their clearance. When we saw Aircraft Y no longer descending above and towards us we executed a go-around. On short final [and] on the second go-around; Tower instructed us to go-around once again due to traffic not clearing the runway fast enough. We landed on the third attempt and had an arrival fuel of 6;080 LB. I got the Tower's phone number and spoke with a Controller who said; 'Yes we saw Aircraft Y was just slightly south of course but he corrected and the second go-around was for traffic.' I told him he was not south of course; he was lined up with the incorrect runway and that's what caused the RA and the Tower dismissed me and said they're not filing a report.The first TCAS RA was handled SOP. Aircraft Y was clearly not lined up with the right parallel runway and it was not just an overshoot of lining up with their final. Because of the TCAS RA command we were able to descend quickly enough away from their lineup and descend to our runway. Our aircraft was in dangerously [in] close proximity to Aircraft Y and we could visually see their trajectory was with our runway. The breakaway from the second TCAS RA was due to the aircraft being at 1200 ft. and visually seeing Aircraft Y start to bank away from our flight path so we were then able to execute a go-around. ATC should have told Aircraft Y to go-around when they heard us responding to a TCAS RA. Aircraft Y was silent the whole time during this event and I suspect it was due to them realizing they were the ones in error. ATC is also in denial when I spoke with them on the phone about the event that caused an aggressive low altitude TCAS RA and two go-arounds. Air carrier Captain reported having to go-around two times due to conflicting traffic.